Network information flow: Gossiping with groups

In this paper, we consider a networking scenario in which a group of nodes wants retrieve a function of another group of nodes data. Here we assume that the function can be cast into a sum of functions of the local variables, a case that subsumes several interesting types of queries. One approach to solve this problem is to route the information from each node to the interested parties one at a time, relaying it over a tree of paths. A second strategy is to reuse the paths when possible, multicasting to the intended recipients the data. A third one, which is the one we are interested in exploring, computes along the routes as well. More specifically, the goal of this paper is to examine how the sought information be forwarded to the intended recipients, computing along the routes by gossiping with selected neighbors. Unlike the context of standard gossiping, in our problem the information needs to flow in a specific direction. In this work we provide a sufficient condition for the convergence to the desired result, and propose a method how to design the information flow for a given network and a problem.